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Simplifying 9x2 + 17x + -29 = -7 Reorder the terms: -29 + 17x + 9x2 = -7 Solving -29 + 17x + 9x2 = -7 Solving for variable 'x'. Reorder the terms: -29 + 7 + 17x + 9x2 = -7 + 7 Combine like terms: -29 + 7 = -22 -22 + 17x + 9x2 = -7 + 7 Combine like terms: -7 + 7 = 0 -22 + 17x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.444444444 + 1.888888889x + x2 = 0 Move the constant term to the right: Add '2.444444444' to each side of the equation. -2.444444444 + 1.888888889x + 2.444444444 + x2 = 0 + 2.444444444 Reorder the terms: -2.444444444 + 2.444444444 + 1.888888889x + x2 = 0 + 2.444444444 Combine like terms: -2.444444444 + 2.444444444 = 0.000000000 0.000000000 + 1.888888889x + x2 = 0 + 2.444444444 1.888888889x + x2 = 0 + 2.444444444 Combine like terms: 0 + 2.444444444 = 2.444444444 1.888888889x + x2 = 2.444444444 The x term is 1.888888889x. Take half its coefficient (0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. 1.888888889x + 0.8919753087 + x2 = 2.444444444 + 0.8919753087 Reorder the terms: 0.8919753087 + 1.888888889x + x2 = 2.444444444 + 0.8919753087 Combine like terms: 2.444444444 + 0.8919753087 = 3.3364197527 0.8919753087 + 1.888888889x + x2 = 3.3364197527 Factor a perfect square on the left side: (x + 0.9444444445)(x + 0.9444444445) = 3.3364197527 Calculate the square root of the right side: 1.826586914 Break this problem into two subproblems by setting (x + 0.9444444445) equal to 1.826586914 and -1.826586914.Subproblem 1
x + 0.9444444445 = 1.826586914 Simplifying x + 0.9444444445 = 1.826586914 Reorder the terms: 0.9444444445 + x = 1.826586914 Solving 0.9444444445 + x = 1.826586914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + x = 1.826586914 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = 1.826586914 + -0.9444444445 x = 1.826586914 + -0.9444444445 Combine like terms: 1.826586914 + -0.9444444445 = 0.8821424695 x = 0.8821424695 Simplifying x = 0.8821424695Subproblem 2
x + 0.9444444445 = -1.826586914 Simplifying x + 0.9444444445 = -1.826586914 Reorder the terms: 0.9444444445 + x = -1.826586914 Solving 0.9444444445 + x = -1.826586914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + x = -1.826586914 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = -1.826586914 + -0.9444444445 x = -1.826586914 + -0.9444444445 Combine like terms: -1.826586914 + -0.9444444445 = -2.7710313585 x = -2.7710313585 Simplifying x = -2.7710313585Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8821424695, -2.7710313585}
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